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X-rays reveal Archimedes secrets
By Jonathan Fildes
Science and technology reporter, BBC News
A series of hidden texts written by the ancient Greek mathematician Archimedes are being revealed by US scientists.
Until now, the pages have remained obscured by paintings and texts laid down on top of the original writings.
Using a non-destructive technique known as X-ray fluorescence, the researchers are able to peer through these later additions to read the underlying text.
The goatskin parchment records key details of Archimedes’ work, considered the foundation of modern mathematics.
The writings include the only Greek version of On Floating Bodies known to exist, and the only surviving ancient copies of The Method of Mechanical Theorems and the Stomachion.
In the treatises, the 3rd Century BC mathematician develops numerical descriptions of the real world.
“Archimedes was like no-one before him,” says Will Noel, curator of manuscripts and rare books at the Walters Art Museum in Baltimore, Maryland and director of the imaging project.
“It just doesn’t get any better than re-reading the mind of one of the greatest figures of Western civilisation.”
‘Eighth wonder’
Revealing Archimedes’ writings presents a huge challenge to the imaging team.
The original texts were transcribed in the 10th Century by an anonymous scribe on to parchment.
Three centuries later a monk in Jerusalem called Johannes Myronas recycled the manuscript to create a palimpsest.
Palimpsesting involves scraping away the original text so the parchments can be used again. To create a book, the monk cut the pages in half and turned them sideways.
To create a book Myronas also used recycled pages from works by the 4th Century Orator Hyperides and other philosophical texts.
Mr Noel describes the palimpsest as “the eighth wonder of the world”.
“You never get three unique palimpsested texts from the ancient world together in one book,” he told the BBC News website. “That’s just completely unheard of.”
The monks filled the recycled pages with Greek Orthodox prayers.
Later, forgers in the 20th Century added gold paintings of religious imagery to try to boost the value of the tome.
The result was the near total obliteration of the original texts apart from faint traces of the ink used by the 10th Century Scribe.
Bright light
Previously the privately-owned palimpsest has been investigated using various optical and digital imaging techniques.
However, much of the text remained hidden behind paint and stains.
The researchers have now turned to a technique known as X-ray fluorescence to tease out the final details of the writings.
The method is used in many branches of science including geology and biology. It has previously been used by other researchers to decode ancient texts.
In August 2005 a team from Cornell University successfully deciphered a series of 2,000-year-old worn down stone inscriptions.
The X-rays are formed in a synchrotron – a particle accelerator that uses electrons travelling at close to the speed of light to generate powerful “synchrotron” light.
The light covers a wide range of the electromagnetic spectrum, including powerful X-rays, a million times more intense than a transmission X-ray used in medical imaging.
“In fluorescence it’s like looking at the stars at night whereas in transmission it’s like looking during the day,” explains Dr Uwe Bergmann of the Stanford Synchrotron Radiation Lab in the US, where the work is being done.
The light enables scientists to look inside matter at the molecular and atomic scale.
Glowing words
The technique is particularly useful for probing the palimpsest because the ink used by the scribe to record Archimedes’ work contains iron.
“When the X-rays hit an iron atom it emits a characteristic radiation, it glows,” says Dr Bergmann. “When you record the glow you can reconstruct an image of all of the iron in the book.”
The glowing words are displayed on a computer screen, giving the researchers the first glimpse of the text in nearly 800 years.
“It’s like receiving a fax from the 3rd Century BC,” said Mr Noel. “It’s the most sensational feeling.”
Each page takes 12 hours to reconstruct as the highly focused beam of X-rays, the width of a human hair, sweeps across the page.
The team has until the 7 August this year to scrutinise the palimpsest, before the synchrotron is switched off for maintenance. During that time they hope to scan between 12 and 14 pages, paying particular attention to the areas covered with the forged paintings.
Eureka! Ancient works by Archimedes rediscovered
The Independent
By Geneviève Roberts
Published: 03 August 2006
A series of previously undiscovered texts by Archimedes, one of the foremost mathematicians of ancient Greece, have been revealed.
Hidden since the 13th century under religious writings and drawings, the single parchment on which they are written is made from goat skin. It includes seven treatises by the mathematician, who was particularly noted for calculating a value for Pi and for being the first recorded person to conceive of infinity.
Will Noel, curator of manuscripts and rare books at the Walters Art Museum in Baltimore, Maryland, and director of the imaging project, described the palimpsest as “the eighth wonder of the world”.
Two of the treatises, “The Method of Mechanical Theorems” and the “Stomachion”, are the only known copies in the world to have survived. The writings also include the only known version of “On Floating Bodies” in Greek.
Dr Noel said: “Editions of most of the great texts of the ancient world, like Homer, Plato and Euclid, came out in the 15th and 16th centuries, which capture most of what they have to say. With this palimpsest we are in the unique and exciting position of making radical additions and corrections to the basic texts of Archimedes in the 21st century. This is only possible with current technology.”
Archimedes’ writings, transcribed in the 10th century by an anonymous scribe on to parchment, are being revealed using a non-destructive technique known as X-ray fluorescence, by scientists in the Stanford Synchrotron Radiation Laboratory in the United States.
In the 13th century, the original manuscript was recycled by a monk in Jerusalem called Johannes Myronas, to create a palimpsest. Using a pumice and lemon juice or milk, the monk faded the writings, cut the parchment in half and rotated the pages. These were then filled by the monks with Greek Orthodox prayers.
Then, in the 20th century, a Parisian art forger added gold paintings of the writers of the four Gospels of the New Testament – Matthew, Mark, Luke and John – to add value to the palimpsest – but nearly obliterated the work of the 10th century scribe.
Dr Noel said that the eight years of work that has been undertaken on the palimpsest has also revealed other ancient texts. Among these is a speech made by Hyperides, an Athenian orator in the 4th century BC and a contemporary of Aristotle and Demostenes.
“It is a speech, probably made in 338BC, at the twilight of the Athenian age of democracy. It concerns Athenian reaction to their loss of a battle against Phillip of Macedon and his son Alexander the Great,” Dr Noel said. In 338BC, the father and son defeated Athens and Thebes.
The privately owned palimpsest, bought by a philanthropist for $2m in 1998 and loaned to the Walters Art Museum, has been investigated previously using optical and digital imaging techniques. But most of the text was indecipherable behind paint. Now, X-ray fluoresence has enabled them to make out the works. Each page takes 12 hours to reconstruct, with X-ray beams the width of a human hair sweeping the pages. As the scientists revealed the first glimpse of the text in 800 years, Dr Noel said the work was “like receiving a fax from the 3rd century BC.”
Eureka! X-ray vision helps decipher Archimedes’s words of wisdom
The Daily Telegraph
By Roger Highfield, Science Editor
03/08/2006
After a millennium in obscurity, the last unreadable pages of the works of Archimedes are being deciphered with the help of one of the brightest sources of X-rays on the planet.
Thanks to the X-ray vision of an instrument at the Stanford Linear Accelerator Centre, SLAC, in California, scholars now have the most complete record of Archimedes’s works to emerge since the middle ages, perhaps explaining for the first time why he really shouted “Eureka!”
A team using a special X-ray imaging technique, called X-ray fluorescence imaging, has studied a goatskin parchment manuscript that records several works of the 3rd century BC mathematician, one of the founders of modern maths, who supposedly shouted “Eureka!” – “I have found it” – upon discovering, while sitting in his bath, how to measure the volume of a solid.
Of all the new revelations, one of the most remarkable is a previously indecipherable page of Archimedes’s treatise On Floating Bodies in Greek, which has significant differences from the known Latin translation and is thought to be much closer to the original. The Eureka moment is probably a myth, said Dr Uwe Bergmann, one of the team. But On Floating Bodies, which discusses how various shapes of bodies float, was a tour de force that could well have merited running naked down the street.
Archimedes extended the boundaries of Greek mathematics, and his place in the history of the related conceptual fields of calculus and of infinity is currently being re-evaluated, said William Noel of the Walters Art Museum in Baltimore and director of the Archimedes Palimpsest collaboration.
In the 10th century, a scribe copied Archimedes’s treatises in the original Greek on to the parchment, marking one of the earliest surviving records of his ideas by about 400 years. But the text presented a monumental challenge for scholars to decode because three centuries later, a monk made the parchment into a palimpsest (a manuscript on which two or more scripts have been written): he scraped away the Archimedes text, cut the pages in half, turned them sideways, and copied Greek Orthodox prayers on to the recycled pages. These writings have therefore been hidden since the 13th century.
Then 20th century forgers painted religious imagery on several pages. The result was the near-obliteration of Archimedes’s work, except for the faintest traces of ink still embedded in the parchment.
In 1998, this unique manuscript was purchased by an anonymous collector who entrusted it to The Walters Art Museum. Though modern imaging techniques did highlight faint traces of original ink, some pages resisted even the most intensive attempts at deciphering. To reveal these writings the intense X-ray beam produced at SLAC’s Stanford Synchrotron Radiation Laboratory has proved invaluable.
“We’re getting a vastly better understanding of one of the greatest minds of all times,” said Dr Bergmann. “We are also showing that it is possible to read completely hidden texts in ancient documents without harming them.”
*13TH CENTURY TEXT HIDES WORDS OF ARCHIMEDES
The pages of a medieval prayer text also contain words of ancient Greek engineer Archimedes. It takes high-tech imaging to read between the lines.*
By Jia-Rui Chong, Los Angeles Times
The book cost $2 million at auction, but large sections are unreadable.
Some of its 348 pages are torn or missing and others are covered with sprawling purple patches of mildew. Sooty edges and water stains indicate a close escape from a fire.
“This manuscript is, by far, the worst of any manuscript I’ve ever seen,” said William Noel, curator of manuscripts for the Walters Art Museum in Baltimore, where it now resides. “It’s a book that is on its last legs.”
The sheepskin parchment originally contained a 10th century Greek text, which was erased by a 13th century scribe who replaced it with prayers. Seven hundred years later, a forger painted gilded pictures of the Evangelists on top of the faded words.
Underneath it all, however, is an exceptional treasure — the oldest surviving copy of works by the ancient Greek mathematician and engineer Archimedes of Syracuse, who lived in the 3rd century BC.
About 80% of the text had been transcribed and translated in the 1910s after it was rediscovered in an Istanbul monastery, but since then much of it became unreadable again because of deterioration.
Fully deciphering its mysteries has had to wait for advanced technologies, some of which had never been applied to ancient manuscripts.
The unusual cast of detectives includes not only the imaging specialists who helped photograph the Dead Sea Scrolls, but also a Stanford University physicist who studies trace metals in spinach with a particle accelerator.
Together, they have been carrying out one of the most remarkable “salvage jobs” in the history of codicology, the study of ancient manuscripts.
Archimedes, it turns out, is only one secret of the text.
Among the mathematicians of antiquity, Archimedes was one of the greatest and most cunning.
He was one of the earliest to devise ways to calculate the area beneath curves and was the first to prove that a circle’s circumference and diameter are related by the constant pi. He developed the Archimedes Screw to lift water and invented deadly devices, such as the Claw of Archimedes, which was designed to grapple enemy warships.
Archimedes died in 212 BC, when Syracuse was sacked by the Romans. Legend holds that he was drawing figures in the sand. “Don’t disturb my circles,” he supposedly told the soldier who killed him.
Knowledge of Archimedes’ work is derived from three books.
Codex A, transcribed around the 9th century, contained seven major treatises in Greek. Codex B, created around the same time, had at least one additional work by Archimedes and survived only in Latin translation.
Codex C has been an enigma.
It was originally copied down in 10th century Constantinople, now known as Istanbul. Three centuries later, the manuscript was in Palestine. By then, it was no longer a precious vestige of ancient learning but an obscure text that could be put to better use as a prayer book.
A scribe began by unbinding the pages. He washed them with citrus juice or milk and sanded them with a pumice stone. He cut the sheets in half, turned them 90 degrees and stitched the new book down the middle.
The scribe wrote prayers over the blank pages. Codex C had become a “palimpsest” — a recycled book.
The book eventually was brought back to Constantinople, where it sat until the 1890s, when a Greek scholar wrote down a fragment of erased text that he was able to read.
That fragment was brought to the attention of Danish philologist Johan Ludvig Heiberg in 1906, then the foremost authority on Archimedes. Armed with a magnifying glass, he translated everything he could read, publishing his work in 1910.
The palimpsest disappeared amid the chaos of World War I, only resurfacing in 1998, when a French family named Guersan offered it for auction at Christie’s in New York. An anonymous book collector paid $2 million and deposited it at the Walters Art Museum for conservation.
Mold had attacked much of the manuscript, and four forged paintings of the Evangelists made in the 20th century covered some of its most important pages.
“That was our worst nightmare,” said Abigail Quandt, senior conservator of rare books and manuscripts at the Walters Art Museum.
Roger L. Easton Jr., a 56-year-old imaging specialist at the Rochester Institute of Technology, had just come off his success revealing hidden text in the Dead Sea Scrolls.
Christie’s had commissioned him to make ultraviolet images of the palimpsest for the auction catalog, and now he offered his help to the museum.
Easton and his colleagues began their work in 2000. They tinkered with different methods for capturing the image with the ultraviolet light, which makes the parchment glow more whitish.
They then merged those images with another set taken under a tungsten light, which enhanced the reddish hue of the Archimedes text. The resulting “pseudocolor” image made it easier to distinguish the black prayer book writing from the burnt sienna words of Archimedes.
Using this painstaking method, Easton and his team took two years to uncover another 15% of the text.
They were stymied in penetrating the rest.
Two more years passed before Stanford physicist Uwe Bergmann, 43, read a magazine article about the Archimedes palimpsest that mentioned it had originally been written with iron gall ink.
One of Bergmann’s projects at Stanford was investigating the process of photosynthesis in plants by using the synchrotron X-rays to image small clusters of manganese atoms in spinach.
“Why not find traces of iron in an ancient book?” he asked.
Bergmann sent an e-mail to the Walters Art Museum, and the museum agreed to a test.
Bergmann set up the palimpsest experiment at the Stanford Synchrotron Radiation Laboratory. Spread over an area the size of a football field, the synchrotron is part of the Stanford Linear Accelerator Center, a Department of Energy facility set in the foothills of Menlo Park.
The synchrotron hurls electrons at near light speed, forcing them to give off X-rays as they veer around bends. That X-ray beam is channeled away into the laboratories.
Bergmann figured the powerful and precise beam could be used to make iron molecules fluoresce, thus allowing him with a sensitive-enough detector to pick up even the faintest traces of ink.
Bergmann first had to determine the exposure time. Too much time and the powerful synchrotron X-ray could damage the parchment. Then, they adjusted the intensity of the beam, which could be so strong that it blinded the detectors that picked up the glow from the iron gall ink.
After two years of refining their technique, Bergmann and his colleagues began the laborious process of imaging the palimpsest this summer.
Each side of a page, mounted in frame that moved in front of the beam, took 12 hours to record. The machines processed the pages continuously for two weeks.
Beneath a moldy, torn painting of St. John emerged two layers of writing.
On the edge of the first page, they saw a signature dated April 14, 1229: “By the hand of presbyter Ioannes Myronas.”
It was the name of the priest who had erased Archimedes.
In an office near Memorial Church at Stanford, Reviel Netz flicked off the lights. Netz, a slight 38-year-old with dark hair, leaned close to the screen of his laptop.
Bergmann’s X-ray work had produced a black-and-white picture of a page from “The Method of Mechanical Theorems,” a text found only in the palimpsest. One phrase — “let them be arranged so they balance on point theta” — had already been translated by Heiberg, although he had had to guess about the word “on,” which was unreadable.
Netz, a professor of classics, looked at the X-ray image and nodded. He smiled.
The actual word was “around.”
“That’s not trivial,” he said, explaining that the change altered the meaning of Archimedes’ calculations involving an object’s center of gravity.
The X-ray image also revealed a section of “The Method” that had been hidden from Heiberg in the fold between pages. It contained part of a discussion on how to calculate the area inside a parabola using a new way of thinking about infinity, Netz said. It appeared to be an early attempt at calculus — nearly 2,000 years before Isaac Newton and Gottfried Wilhelm Leibniz invented the field.
The discoveries may seem small, but they are significant in the understanding of ancient mathematics, Netz said.
One passage he studied several years ago involved the innumerable slices and lines that could be made from a triangular prism similar to a wedge of cheese. Netz said the passage, which was unreadable to Heiberg, showed that Archimedes was grappling with the concept of infinity long before other mathematicians.
For Netz, a specialist in ancient mathematics and cognitive history, the chance to decipher the palimpsest “is the fulfillment of an incredible dream,” he said.
One of his biggest breakthroughs involves a quirky part of the palimpsest called the “Stomachion,” which literally means “Belly-Teaser.”
Stomachions were children’s games in which 14 geometrical shapes were rearranged to create new shapes. Heiberg translated fragments of the manuscript but paid little attention to it, thinking it was just a game.
Netz saw a deeper significance. Archimedes asked a more restricted question in his “Stomachion”: How many different ways could you combine the 14 triangles to make a square?
Netz believes the fragments address an area of mathematics known as combinatorics that scholars have only recently believed interested the Greeks.
For all the high-tech efforts, there are still gaps remaining in the Archimedes text, perhaps 2%, Netz guessed.
Among the jumbled fragments are clues that perhaps the deepest secrets are yet to be found.
A century ago, Heiberg copied down two lines that he couldn’t identify. They began: “The youngest had been abroad for so long that the sisters wouldn’t even know who was who.”
The passage was not Archimedes.
In 2002, scholars were able to cross-reference the quote. It came from “Against Timandros,” written by a 4th century BC Athenian orator named Hyperides.
Although Hyperides is little-known now, contemporaries frequently compared him to Demosthenes, an acknowledged master of oratory.
No complete versions exist of “Against Timandros,” which Hyperides had written as part of a lawsuit over an inheritance, said Judson Herrman, a classicist at Allegheny College in Pennsylvania.
Further study determined there were 20 pages of Hyperides in the palimpsest, including a previously unknown text called “Against Diondas.”
The palimpsest, it turns out, took parchment from seven texts, including what are believed to be a commentary on Aristotle’s “On the Soul” and a group of biographies of the saints, plus two still unidentified texts.
The works are even more difficult to discern than the Archimedes because the ink is different and the pages more thoroughly scrubbed.
“I have been cursing all morning,” Herrman said of his work on a few lines of Hyperides.
The scientists aren’t giving up.
Easton’s team recently began experimenting with precisely tuned light-emitting diodes, or LEDs, to illuminate the text. The team also is using angled light to detect the outlines of letters etched in the parchment by the acid in the ink.
The team made progress on a few pages, but it may take decades — or longer — before technologies are developed that can unveil all the texts.
“We’ll probably leave something for future scientists to work on,” Netz said.
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